Crush chiles, garlic, and salt in a mortar to form a paste. (Alternatively, mince chiles and garlic together, sprinkle with salt, and mash with flat side of a chef's knife.) Scrape into a bowl. Stir in bread crumbs, then blend in yolks and stock.
Add oil drop by drop to chile mixture, beating on low speed with an electric mixer, until it starts to thicken. Increase the pour of oil to a thin stream, beating constantly, until a mayonnaise-like mixture forms. Preheat oven to 225°.
Arrange baguette slices in a single layer on 2 baking sheets. Bake until dry but not golden, about 20 minutes, turning once.
Make ahead: Rouille, up to 4 days, chilled. Baguette toasts, up to 3 days, stored airtight at room temperature.
Do while fish marinates and stock simmers.